A model must be judged on the basis of its ability to explain and predict experimental observations. We believe the model presented in this paper for the growth process and resultant morphology has been shown to be capable of explaining a wide variety of experimental observations by a number of different investigators. The assumption is that fiber crystals, once nucleated in an extensional flow field, continue to grow by a chain attachment process in which the highest molecular weight material forms the continuous growth core. Further growth is obtained by the extension and flattening of chains tied to the central backbone and acted upon by the fluid mechanical forces in the shearing flow boundary layer surrounding the growing crystal. A central feature of the model is the realization that complete chain extension and crystallization is not possible due to energetics considerations, and the growing fiber thus must consist of a chain backbone surrounded by a uniform “fuzz” of uncrystallized coils which are attached to the main fiber. The final morphology and properties of the crystals which result from this growth process can then be explained on the basis of this understanding of the growth kinetics.